As a response to stringent emission requirements being set for internal combustion engines, engineers are developing apparata and methods to help reduce vehicle tailpipe emissions. These have included such apparata and methods as closed-loop feedback control on air/fuel ratio in order to take advantage of catalyst characteristics, and various forms of port and throttle body fuel injection. In modern research engines other apparata and methods are being investigated in order to reduce unwanted emissions to an even lower level. Many of these new apparata and methods seek new ways of controlling combustion quality, which has a direct influence on engine emissions. However, in order to influence combustion quality with the result of obtaining desired tailpipe emissions, some effective and robust means for diagnosing combustion quality is needed. With such means, engineers can better investigate the effects of varying the engine control parameters on combustion quality and develop an effective control strategy, and/or implement such means in the engine's diagnostics/controls systems.
One method of assessing combustion quality is to monitor engine speed and/or acceleration in the time domain. Aberrational changes in speed and acceleration can indicate the presence of engine misfires. If aberrations are detected, engine diagnostics/controls systems can respond by influencing engine behavior to reduce or prevent further misfire. However, as will be discussed below, there are practical problems with properly diagnosing misfires in time-domain speed/acceleration data. Before discussing these problems in detail, it is first valuable to review the dynamic behavior of engines.
The two most common engine dynamics models are the constant inertia model and the time-varying inertia model, each of which are well-known expressions of Newton's 2nd law. The constant inertia model can be expressed as follows: ##EQU1##
where
J represents an estimated constant polar moment of inertia of the engine about the crankshaft axis (generally the average value of J(.theta.), though other values can be used); PA1 .theta. is the crankshaft rotation angle; PA1 P is the cylinder pressure; PA1 V is the cylinder volume; and PA1 n is the number of cylinders. PA1 J(.theta.) represents the actual crankangle-varying polar moment of inertia of the piston and its slider-crank mechanism (the connecting rod and crankshaft, though any other rotational inertias can be included as well); PA1 .theta. is the crankshaft rotation angle; PA1 P is the cylinder pressure; PA1 V is the cylinder volume; and PA1 n is the number of cylinders.
The final two summations in equation (1) represent friction and pumping torques as well as all other external torques applied to the crankshaft.
The time-varying inertia model may be expressed as follows: ##EQU2##
where
Friction, pumping, and external torques are also taken into account in equation (2).
These models can be used to calculate estimated speed and acceleration data in a real engine. In the real engine, pressure may be measured using quartz piezoelectric transducers or other pressure sensors, and J, J(.theta.), and V may all be calculated if the engine geometry is known. These values may then be used in equations (1) and (2) to solve for speed .theta. and acceleration .theta.. Plots of calculated speed and acceleration over time for an exemplary four-cylinder, four-stroke internal combustion engine operating at low nominal speed (around 2100 RPM) are shown for both models in FIGS. 1 and 2. (Note that the friction, pumping, and external torques from equations (1) and (2) were assumed to be constant, though they need not be constant to implement equations (1) and (2) and are expected not to be constant in a vehicle.)
FIG. 1 illustrates the roughly sinusoidal variation in calculated engine speed about the nominal (average) engine speed as the crankshaft turns. FIG. 2 similarly illustrates engine acceleration, which generates a roughly sawtooth trace varying about zero. As the engine approaches top dead center of the compression stroke for one of the four cylinders at .theta.=n .multidot.180.degree. (n is an integer), the crankshaft slows down because it has to do work on the gas during compression (i.e., the kinetic energy of the crankshaft is converted into potential energy in the cylinder gas). After top dead center, the engine accelerates because the power stroke (expansion/work stroke) has begun and combustion gases are working on the crankshaft.
Except for a small offset in speed, the speed and acceleration waveforms from the two models are quite similar. This is to be expected because equation (2) approximates equation (1) at low engine speeds, the difference between the results of the models largely being due to the inertia of equation (2) varying with crankshaft angle. These inertial effects are nearly linear at low speed. In comparison to actual experimental data (not shown), the calculated speed and acceleration shown on the plots of FIGS. 1 and 2 are quite close to experimental data with the exception that the constant inertia model predicts a high (and inaccurate) speed in comparison to the time-varying inertia model. This makes the constant inertia model generally unsuitable for use in calculating speed for application in feedback control. The time-varying inertia model can be considered as providing an accurate depiction of experimental data.
FIGS. 3 and 4 then show the speed and acceleration calculated using the constant and time-varying inertia models using cylinder pressure profiles taken from the same engine at a higher nominal engine speed, approximately 4000 rpm. The magnitude and shape of the speed and acceleration plots for the constant inertia model (equation (1)) are not significantly changed from the results at 2100 rpm. This is to be expected from equation (1), which is not speed-dependent--it will produce similar-appearing waveforms regardless of the nominal engine speed. However, the plots of calculated speed and acceleration for the time-varying model (equation (2)) look drastically different from those at lower nominal engine speed. This is because in equation (2), rotational acceleration .theta. depends on both the crankshaft angle as well as its speed squared .theta..sup.2. Therefore, as the nominal engine speed is varied, the speed and acceleration plots for equation (2) will change significantly in magnitude and shape. Looking to the plots for the time-varying inertia model, the dominant speed waveform appears to be out of phase with that of the calculated speed for the constant inertia model, and the engine appears to speed up during part of the compression stroke. This is because the speed-squared term becomes very large in the time-varying inertia model (and in an actual engine), and the rate of inertia change decreases as the engine approaches top dead center at .theta.=n .multidot.180.degree.. The acceleration profile for the time-varying inertia model looks almost like a sinusoid with a sharp positive peak following top dead center. The sinusoidal waveform comes from the .delta.J(.theta.)/.delta..theta. term, with the positive peaks resulting from superimposed combustion energy accelerating the crankshaft. In comparison to experimental data, the results of the time-varying inertia model are still generally accurate, but the results of the constant inertia model are grossly inaccurate.
When designing engine diagnostics/control systems, a speed or acceleration trace such as that produced by the constant inertia model is desirable because it has fairly uniform shape and magnitude at all nominal engine speeds. It would thus be fairly easy to detect aberrations such as those caused by misfire, as by using analog and/or digital control elements to detect abnormal rates of velocity/acceleration change, or by otherwise detecting telltale signs of misfiring. Unfortunately, as noted above the constant inertia model is more valuable as a theoretical tool than a practical one: its results grow inaccurate as nominal engine speed increases, and thus it cannot serve as a good indicator of combustion quality for control purposes. As for the time-varying inertia model, it can accurately indicate combustion quality across a wide range of nominal engine speeds, but the behavior variations in predicted speed and acceleration across this speed range makes it difficult to design a robust control system for qualitatively evaluating combustion quality. In other words, it is difficult to design a diagnostics/control system using the time-varying inertia model (i.e., the actual engine configuration) that can consistently distinguish misfires from standard engine behavior when the engine behavior changes from that depicted in FIGS. 1 and 2 to that of FIGS. 3 and 4.